Question

Factorise
(1) — x³-2x²-x+2
(2)— x³-3x²-9x-5
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Answer 1

Answer:

Question :-

(1) x³ - 2x² - x + 2

Formula used :-

➪ a² - b²

➭ (a + b) (a - b)

Solution :-

➪ x³ - 2x² - x + 2

➭ x²(x - 2) - 1(x - 2)

➭ (x - 2) (x² - 1)

➭ (x - 2) {(x)² - (1)²}

➭ (x - 2) (x + 1) (x - 1)

∴ The value of x³ - 2x² - x + 2 is

(x - 2) (x + 1) (x - 1)

Question :-

2) x³ - 3x² - 9x - 5

Solution :-

➪ x³ - 3x² - 9x - 5

➭ x³ + x² - 4x² - 4x - 5x - 5

➭ x²(x + 1) - 4x (x + 1) - 5(x + 1)

➭ (x + 1) (x² - 4x - 5) [ Taking (x + 1) common ]

➭ (x + 1) {x² - (5 - 1)x - 5}

➭ (x + 1) {x² - 5x + x - 5}

➭ (x + 1) {x(x - 5) + 1(x - 5)}

➭ (x + 1) (x - 5) (x + 1)

➭ (x + 1)² (x - 5)

∴ The value of x³ - 3x² - 9x - 5 is

(x + 1)² (x - 5)